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arXiv:2608.29079

Quantum discord of Gaussian states in non-inertial frames

Siwei Li, Xiaofen Huang

quant-phSubmitted Aug 29, 2026• Announced Sep 1, 2026• 0 citations
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Abstract

We investigate the redistribution of continuous-variable Gaussian quantum discord under the Unruh effect for both one and two uniformly accelerated observers. The discord shared between the inertial mode and the accessible accelerated mode, as well as that between the two accessible accelerated modes, decays monotonically with acceleration and vanishes in the limit $a\to\infty$, while the Unruh effect generates discord in all causally disconnected Rindler mode pairs. The initial quantum correlation is therefore redistributed across Rindler partitions rather than destroyed. We further characterize how the squeezing parameter $s$ and field frequency $ω$ control the discord in different mode-pair classes. For causally connected pairs, $s$ and $ω$ exert comparable, interchangeable effects; for cross-region pairs, the squeezing parameter dominates; and for intra-observer cross-region pairs, the field frequency is more influential. In the two-observer case, the $A_{II}$-$B_{II}$ pair exhibits non-monotonic behavior with a peak whose position shifts to larger $a$ as $ω$ increases, and both parameters contribute only weakly except near an optimal $\fracω{s}$ ratio.

Comments
11 pages, 31 figures

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We investigate the redistribution of continuous-variable Gaussian quantum discord under the Unruh effect for both one and two uniformly accelerated observers. The discord shared between the inertial mode and the accessible accelerated mode, as well as that between the two accessible accelerated modes, decays monotonically with acceleration and vanishes in the limit a→∞a\to\inftya→∞, while the Unruh effect generates discord in all causally disconnected Rindler mode pairs. The initial quantum correlation is therefore redistributed across Rindler partitions rather than destroyed. We further characterize how the squeezing parameter sss and field frequency ωωω control the discord in different mode-pair classes. For causally connected pairs, sss and ωωω exert comparable, interchangeable effects; for cross-region pairs, the squeezing parameter dominates; and for intra-observer cross-region pairs, the field frequency is more influential. In the two-observer case, the AIIA_{II}AII​-BIIB_{II}BII​ pair exhibits non-monotonic behavior with a peak whose position shifts to larger aaa as ωωω increases, and both parameters contribute only weakly except near an optimal ωs\fracω{s}sω​ ratio.
We study the distribution of entanglement between modes of a free scalar field from the perspective of observers in uniform acceleration. We consider a two-mode squeezed state of the field from an inertial perspective, and analytically study the degradation of entanglement due to the Unruh effect, in the cases of either one or both observers undergoing uniform acceleration. We find that, for two observers undergoing finite acceleration, the entanglement vanishes between the lowest-frequency modes. The loss of entanglement is precisely explained as a redistribution of the inertial entanglement into multipartite quantum correlations among accessible and inaccessible modes from a noninertial perspective. We show that classical correlations are also lost from the perspective of two accelerated observers but conserved if one of the observers remains inertial.
A uniformly accelerated observer perceives the Minkowski vacuum as a thermal bath, so acceleration acts as a noise channel on correlations shared with an inertial partner. For a Dirac field in the standard treatment, the resulting map is a one-sided amplitude-damping channel, and entanglement and quantum discord survive at infinite acceleration. We introduce a symmetric Unruh-like map in which the vacuum and the one-particle state both exchange amplitude with the inaccessible Rindler region; for a Bell state it yields a bit-flip channel whose flip probability is the Fermi-Dirac occupation at the Unruh temperature. Using negativity, mutual information, and all six pairwise quantum discords, we find that the entanglement and discord between the inertial observer and the accessible mode vanish together at infinite acceleration, leaving only one bit of classical correlation. These results show that the fate of quantum correlations in noninertial frames depends on the structure of the Minkowski-Rindler map.
We investigate the redistribution of continuous-variable quantum discord within the framework of an expanding universe. We find that quantum discord exhibits stronger sensitivity to the spacetime expansion rate than to the expansion volume. As both the expansion rate and expansion volume increase, the initial quantum discord shared by the two bosonic modes decays, while quantum discord is induced in additional mode pairs by the underlying spacetime expansion, signaling a global redistribution of quantum correlations across the system. Specifically, the induced discord is largest for cross-observer bosonic-antibosonic pairs, followed by same-observer bosonic-antibosonic pairs, and smallest for the pair of antibosonic modes. Furthermore, our quantum discord analysis demonstrates that particles with lower momentum and optimal mass serve as more favorable candidates for extracting information about the expanding universe. This work substantially enriches the theoretical framework of quantum discord in expanding spacetimes, and provides new perspectives as well as a solid theoretical foundation for further investigations.
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We review a recently introduced unified approach to the analytical quantification of correlations in Gaussian states of bosonic scalar fields by means of Renyi-2 entropy. This allows us to obtain handy formulae for classical, quantum, total correlations, as well as bipartite and multipartite entanglement. We apply our techniques to the study of correlations between two modes of a scalar field as described by observers in different states of motion. When one or both observers are in uniform acceleration, the quantum and classical correlations are degraded differently by the Unruh effect, depending on which mode is detected. Residual quantum correlations, in the form of quantum discord without entanglement, may survive in the limit of an infinitely accelerated observer Rob, provided they are revealed in a measurement performed by the inertial Alice.
We calculate the quantum discord between two free modes of a scalar field, which start in a maximally entangled state and then undergo a relative constant acceleration. In a regime where there is no distillable entanglement due to the Unruh effect, we show that there is a finite amount of quantum discord, which is a measure of purely quantum correlations in a state over and above quantum entanglement. Even in the limit of infinite acceleration of the observer detecting one of the modes, we provide evidence for a nonzero amount of purely quantum correlations. We discuss our result in the context of secure quantum communications involving eavesdroppers in noninertial frames.